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Dingan

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Trends
« on: March 25, 2016, 10:53:08 pm »
+34

Here's a little project I've been working on :) ...

0 Introduction

Somewhat-inspired by threads like this, I got to wondering: Why do our opinions of Dominion change over time?  Is it simply because we get better and more experienced at it?  Or are there actual objective reasons as to why we think Sea Hag is not as good as it used to be?  Or why Urchin is getting better?  What follows in this post is an attempt to answer (part of) that.

(Ok, tbh, it doesn't really answer much, if anything at all.  I mostly plotted these things out of pure curiosity.  Take it or leave it :) )

Every section below shows a function y(x), where x is expansion set (Base, Intrigue, etc.).  For each section, I explain what y is, my method of counting things, any assumptions I made, etc.  I then remark on any observations I see in the data, although I try not to draw too many conclusions.  Feel free to come up with your own though (and talk about them).

These are some things that apply to all sections:
  • I took every expansion and promo into account up to and including Summon
  • I got the data mostly from the wiki
  • The x-axes are to-scale.  That is, Base came out Oct. of 2008, Intrigue came out July of 2009, etc., and the horizontal distances between the data points are proportional to how much time is actually between those dates.
  • I didn't really know where to put promos on the x-axes.  I could have put them each on their own release date, but I decided against that because (1) that would clutter up the graphs, and (2) it doesn't really make sense to talk about the ratio of a in b, where b is only 1.  This will make more sense when you see what the graphs are of.  So I lumped all promos together, and have them as released on Aug. of 2015 which is, as far as I could tell, about the release of Summon.  I've marked each data point for promos in red to indicate this inconsistency.
  • I used my best judgement in cases when it wasn't clear what to count something as.  For example, is Tribute a village-variant?  And what about Knights?  Etc.  If anything doesn't make sense, or you want more explanation, or you disagree with how I did something, or whatever, then feel free to message me.
Without further dudes...

1 Number of Cards

First off, an easy one: the number of cards in each set.  I indicate (1) how many randomizers there are, and (2) how many extra cards that the set came with that could possibly contribute to Fairgrounds.  This means I counted Province, Duchy, Gold, etc. for Base.



We all knew Dark Ages and Adventures were the big ones.  So not much else to explain or conclude here.

2 Average Coin Cost of Supply Card

One data point here is the average coin cost of the randomizer cards in the set.  I don't do anything with Potion cost.  If something cost x* (Peddler, Doctor, ...) I counted it as x.  I counted Knights as $4.9.



Looks like this is an incredibly flat curve, with the exception of 3 points.  Alchemy had Potions, and so it makes sense they have a low average coin cost.  DX can charge whatever the heck he wants for Promos.  Prosperity, however, is the 1 true outlier -- even counting Peddler as $0 instead of $8, this would still be by far the most expensive set.  Huh.  Oh and it also has GM.

3 Percentage of Attacks

For each set, I show the percentage of randomizers that are (1) a junking attach, (2) a hand-size-reducer attack, and (3) any other type of attack.  For things like Torturer that are 2 of these things, I used my best judgment to put them into the 1 thing they are used more often as.  I counted Travellers as attacks because at least one of (each of) them are.



Again, not much to report on.  This appears to be fluctuating but doesn't show a trend upwards or down.

4 Percentage of Thinners

Figured percentage of junkers was a good segway into showing the percentage of thinners in each set.  Again, I used my best judgement for counting things; like, I didn't count Knights (Dame Anna), but I did count Transmute.  Randomizers only.



This is also not trending up or down per se, but it definitely has am up-and-down periodicity to it.  Mind: blown.

5 Percentage of Village- or TR-Variants

Basically, if something had a "+2 Actions" clause or similar on it, I counted it.  Or, if it didn't have a + actions, but it could still typically be used to gain actions -- so things like Ironmonger, Herald, etc.  I think I didn't count things like Tribute and Tournament (Trusty Steed), although honestly I don't even remember haha.  Randomizers only.



This seems to be ever-so-slightly trending upwards.  Guess DX does like giving us more of this type of engine component.

6 Percentage of Alt-VP Cards (Not VP-Token Cards)

Pretty self-explanatory -- I counted things like Gardens, Great Hall, Nobles, etc.  Randomizers only.



Looks like it's ever-so-slightly trending downwards.  Not much else to say.

7 Card/Event Artwork Genders

This was a fun one.  This shows the percentage of any card art (so randomizers, non-supply cards, and Events) that has primarily (1) females on it, or (2) males on it, or (3) neither/both/I couldn't tell.  I used my eyes to determine this and didn't look on any rulebooks or anything, so I may have gotten some of it wrong.  But I did my best.



DX, we need more chicas!!  And I now see why the Dark Ages were so dark :P

8 Number of Big Horizontal Lines

This shows the number of big horizontal lines (like in Nobles, Young Witch, etc.) in each set.  I believe I counted everything, not just randomizers.



Obviously trending upwards.  Does this mean Dominion is getting more complicated?  More things to remember at times other than when you play a card?  ???

9 Average Number of Types Per Card

This shows the average number of types per card.  By "Types", I mean the number of things on the bottom of the card (that's what a Type is, right?).  So like Great Hall is 2 types (Action, Victory), Marauder is 3 (Action, Attack, Looter), etc.  For cards that had extra non-randomizer things to them, I counted the UNION of all the types associated to the randomizer.  So like Tournament had 4 (Action, Prize, Attack, Treasure), Knights had 4 (Action, Knight, Attack, Victory), and so on.



Again, a pretty clear upward trend.  Dang you DX for making this game more complicated!  :P  Pretty wild that there are almost on average 2 types per card in Adventures.  Interesting note though: Promos are said to be "exotic", yet they have the lowest number types per card.

10 Average Length of Card Text

This is my favorite one.  It also was a pain in the a** to do though.  The "length" of a card is the number of characters in the string that composes that card's explanation text.  I didn't count the card's types or their name.  I used sites like this to copy the card text, then I'd paste it into some string-length-calculator, then average those out for the set (but I did have to type it all out for Adventures because one of those sites does not exist for Adventures yet :().  For cards that have extra non-randomizer cards, I took the SUM of all of the text.  So like Tournament and Travellers had a lot each, which kind of skewed the average.  But I figured this was best because in order to fully understand those cards, you need to read all that text.  I didn't include Events.



Once again, an obvious upwards trend.  Oh, how the days are gone where you only needed a 3rd grade reading level to fully understand Dominion :(

11 Conclusion

That's it.  Thanks for watching!  To sum up: Dominion is getting more complicated.  And there aren't enough chicks (in the card art).

As a final aside: All the images above are being hosted on a third party site.  Let me know if their links ever break or whatever.
« Last Edit: March 31, 2016, 02:48:46 am by Dingan »
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Re: Trends
« Reply #1 on: March 25, 2016, 11:09:40 pm »
0

I love data collection. This is awesome
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Beyond Awesome

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Re: Trends
« Reply #2 on: March 26, 2016, 03:08:04 am »
+7

Most of the charts are shown up as broken images to me. I can't see them.
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Dingan

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Re: Trends
« Reply #3 on: March 26, 2016, 03:42:33 am »
0

Most of the charts are shown up as broken images to me. I can't see them.

I noticed that happens on my phone, but not on desktops.  I'll look into it.
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Accatitippi

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Re: Trends
« Reply #4 on: March 26, 2016, 06:24:45 am »
+1

Most of the charts are shown up as broken images to me. I can't see them.

I noticed that happens on my phone, but not on desktops.  I'll look into it.

This happens on my laptop too.  :-\
I'm using Firefox, if that's any help.

This is great!
But it would be cool to have a plot of the same varables considering the whole of Dominion (instead of single expansions) on a time axis. That way it would be easier to "see" the state of the game at every time point, and thus make better hypotheses about trends and stuff. :)
Then it would also be possible to add promos to their correct release time :)
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werothegreat

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Re: Trends
« Reply #5 on: March 26, 2016, 10:24:36 am »
0

Most of the charts are shown up as broken images to me. I can't see them.

Likewise.  Also, the text of each card is printed in their infobox on the wiki, including for Adventures, which you can totally copy-paste from.
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Dingan

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Re: Trends
« Reply #6 on: March 26, 2016, 02:36:53 pm »
0

Huh, now they work on my phone.  No idea haha.  They're just images.  Nothing special about them.  Maybe it fixed itself?
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faust

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Re: Trends
« Reply #7 on: March 26, 2016, 05:57:57 pm »
0

Huh, now they work on my phone.  No idea haha.  They're just images.  Nothing special about them.  Maybe it fixed itself?

It's still not working for me (only some of them). I'm using Firefox.
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Dingan

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Re: Trends
« Reply #8 on: March 28, 2016, 04:39:00 pm »
+1

I moved the chart images to a different site.  Let me know if they're still broken for anyone.  Looks fixed on my phone.  Seems like the images were broken when my phone was connected to 4G, but not broken when connected to wifi.  Haha.  No idea.  Whatev.
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JW

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Re: Trends
« Reply #9 on: March 28, 2016, 04:53:38 pm »
0

This is great. Have you considered adding cumulative running totals? For example, this could show how the percentage of Village-variants among all cards has changed as sets have been released.
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Dingan

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Re: Trends
« Reply #10 on: March 28, 2016, 04:57:08 pm »
0

This is great. Have you considered adding cumulative running totals? For example, this could show how the percentage of Village-variants among all cards has changed as sets have been released.

http://forum.dominionstrategy.com/index.php?topic=14649.msg563604#msg563604

I thought about doing that for all the charts, but decided against it.  I guess it could be easily done with the data I already have though, because we know how many cards are in each set.  But meh.
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wachsmuth

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Re: Trends
« Reply #11 on: March 28, 2016, 06:58:39 pm »
0

Is your data on the number of types in Guilds correct? Only two cards even have more than 1 type in that whole set, namely Taxman and Soothsayer. There's just no way that the average is more than 1.5, unless you count things like 'overpay' or 'coin token' as a separate type, which they are usually not counted as.
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Dingan

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Re: Trends
« Reply #12 on: March 28, 2016, 07:15:15 pm »
0

Is your data on the number of types in Guilds correct? Only two cards even have more than 1 type in that whole set, namely Taxman and Soothsayer. There's just no way that the average is more than 1.5, unless you count things like 'overpay' or 'coin token' as a separate type, which they are usually not counted as.

Hmm, must have just been an error.  My spreadsheet says 1.53.  I'll fix it.
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Re: Trends
« Reply #13 on: March 28, 2016, 10:17:53 pm »
0

Alchemy has the same number of villages + Throne Room variants as Attacks.
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Davio

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Re: Trends
« Reply #14 on: March 29, 2016, 06:13:26 am »
+1

I think you can probably put a number on the Complexity of a card, for example:

If the card only has vanilla bonuses in the form of +X Y where X is a number and Y is either Cards, Actions, Coins or Buys, complexity starts at 0.
If the card only has calculated vanilla bonuses in the form of +X Y where X is a simple formula (for instance Philosopher's Stone, Bank), complexity starts at 5.
Otherwise, complexity starts at 10.

Add 5 for each main type it has (I consider Action, Victory and Treasure to be the main types); only Hovel doesn't have a main type.
Add 5 for each subtype it has (I consider Reaction, Attack, Duration, Prize, Knight, Ruins, Shelter, Looter, Reserve and Traveller to be subtypes).

If the card has 2 parts where the 2nd part isn't covered by its subtype, add 5. With Duration and Reaction cards there often is a connection with the 2nd part, so we don't count this twice. Examples include Trade Route (extra setup), Grand Market (buy restriction), Royal Seal (on-gain which isn't a Reaction), Goons, Peddler, etc.

If the card has a Potion included with its cost, add 5.

Count the number of characters in the card text, add its square root, rounded down.

If adding the card to the supply causes other cards to be added (either to the supply or outside of it) that are not covered by its subtypes, add 5.
Looters (subtype) which add Ruins don't count for this condition, but this does include Hermit (adds Madman) and Urchin (adds Mercenary).

Example 1: Smithy
Complexity = 0 (only vanilla bonuses) + 5 (just an Action) + 3 (sqr rt) = 8

Example 2: Scrying Pool
Complexity = 10 (base) + 10 (Action + Attack) + 5 (Potion) + 16 (sqr rt) = 41

Example 3: Hermit
Complexity = 10 (base) + 5 (Action) + 16 (sqr rt) + 5 (extra card pile outside of supply) = 36
« Last Edit: March 29, 2016, 06:17:59 am by Davio »
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Re: Trends
« Reply #15 on: March 29, 2016, 06:34:47 pm »
0

I think with Hermit though you need to factor in Madman with the complexity factor. This especially hike true for Travellers
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Re: Trends
« Reply #16 on: March 29, 2016, 06:54:58 pm »
0

As more and more Dominion cards get released, I'm finding more and more often there will only be one or zero villages most MF games in random sets, just due to the vast amount of cards.
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Re: Trends
« Reply #17 on: March 30, 2016, 12:04:29 am »
+2

As more and more Dominion cards get released, I'm finding more and more often there will only be one or zero villages most MF games in random sets, just due to the vast amount of cards.
Since the fraction of cards which are villages has been slightly increasing. this cannot be correct. As in, there's no way you're seeing fewer villages because more sets have been released.
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Re: Trends
« Reply #18 on: March 30, 2016, 12:27:22 am »
+3

As more and more Dominion cards get released, I'm finding more and more often there will only be one or zero villages most MF games in random sets, just due to the vast amount of cards.
Since the fraction of cards which are villages has been slightly increasing. this cannot be correct. As in, there's no way you're seeing fewer villages because more sets have been released.

He didn't say he was seeing fewer villages on average. He said he's seeing more games with no villages. That is absolutely a result of a larger card pool.
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ConMan

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Re: Trends
« Reply #19 on: March 30, 2016, 01:52:35 am »
+10

Using some rough calculations of my own, taking as following (based on a very quick classification of a list I'd been planning to use for something else, counts will differ because things are classified a little oddly in places):

Expansion# Kingdom cards# VillagesProportionCumulative # Kingdom cardsCumulative # VillagesProportion
Base2530.122530.12
Intrigue2520.085050.10
Seaside2640.157690.12
Alchemy1220.1788110.13
Prosperity2530.12113140.12
Cornucopia1320.15126160.13
Hinterlands2630.12152190.13
Dark Ages3560.17187250.13
Guilds1320.15200270.14
Adventures2940.14229310.14

That's not including Events, Dame Molly, Trusty Steed, or cards that are potential targets for upgrading like Madman or Disciple. Also I'm skipping the promos.

Then, assuming that a kingdom is 10 cards randomly drawn from the available pool (so again, ignoring Events and Young Witch):

ExpansionCumulative # Kingdoms# Kingdoms with 0 VillagesProportion
Base3,268,760646,6460.198
Intrigue10,272,278,1703,190,187,2860.311
Seaside954,526,728,530247,994,680,6480.260
Alchemy4,513,667,845,8961,096,993,404,4300.243
Prosperity62,088,566,355,81615,579,278,510,7960.251
Cornucopia192,657,357,567,67546,897,636,623,9810.243
Hinterlands1,340,705,736,329,960337,429,331,439,2000.252
Dark Ages11,280,482,088,242,1002,584,164,477,130,2400.229
Guilds22,451,004,309,013,3005,076,973,385,101,0500.226
Adventures89,545,738,240,627,30020,256,672,480,820,8000.226

So in fact, the proportion of games with no villages has mainly been dropping, but not by a lot - it's been staying at around 22-24% of games.
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Re: Trends
« Reply #20 on: March 30, 2016, 02:11:26 am »
+2

Great post, one thing that looks out of place is that Intrigue should have 3 plus actions, mining village, shanty town, and nobles (though Nobles is an expensive Necropolis sometimes that's what you get it for).
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Re: Trends
« Reply #21 on: March 30, 2016, 02:52:54 am »
0

I agree with JW, I would count Nobles as a Village. I also think Events should be included as should Disciple/Teacher and also Champion. So, 3 more villages for Adventures. Champion is like a Village on steriods.

I agree about ignoring Dame Molly though.
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Re: Trends
« Reply #22 on: March 30, 2016, 02:13:38 pm »
+1

There's also Necropolis. Sometimes that's all the villages you need.
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Re: Trends
« Reply #23 on: March 30, 2016, 05:41:45 pm »
0

Yep, I missed Nobles somehow but would have counted it otherwise. I can redo the calculations including Page and Peasant as "sources" of Villages, and if I do that I'd probably include Hermit as well. Events are trickier because they effect the number of possible Kingdoms in a more complicated way than I can calculate using a single Excel function call. I could hack something together in R, but that was more than I had time for yesterday.
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Re: Trends
« Reply #24 on: March 30, 2016, 05:53:25 pm »
0

Events are trickier because they effect the number of possible Kingdoms in a more complicated way than I can calculate using a single Excel function call. I could hack something together in R, but that was more than I had time for yesterday.

If Lost Arts is the only event that qualifies as +Actions, you just need to know the chance that Lost Arts shows up in a given Kingdom. Assuming 10 cards kingdoms and no limit on the number of events used in a kingdom, the answer is just 10 / # of Kingdom cards you have to choose from. This is the chance that an otherwise +Action-less Kingdom gets changed to effectively being a +Actions Kingdom by Lost Arts.

Even accounting for a 2 event limit in a kingdom should not change things much, more detail below if anyone is interested.

With a 2 event limit, you can't simply look at the chance that a certain event comes up before you draw 10 kingdom cards alone. You also need to know whether it is the first or second event, as future events won't be used.

Fortunately, every event has an equal probability of showing up, so if you calculate the average number of events that show up in a game, then that number is divided evenly among the 20 (21 with Summon) events. You can determine the distribution of the number of events that show up with the negative hypergeometric distribution. As of Adventures and 20 events, jonts26 did the following calculation of the chance for different numbers of events (I believe assuming 235 Kingdom cards).

I should have actually used negative hyper geometric instead of a naive binomial in my last post. Real probabilities are (for all cards):

0 events: 43.5%
1 event: 35.5%
2+ events: 21.0%

This, if I'm not wrong, gives:
0.355*1/20+0.21*2/20=3.875% chance of drawing a specific event as the only event or as one of the first two events.
This gives a 0.4% deviation from the unadjusted value of 10/236.
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